Transformers build up magnetic flux in the core and saturate, they can help act like a 'flywheel' (supposedly), like a energy storage, and could potentially help smooth out voltage or current fluctuations (also known to help balance loads between legs), which could help with the load sensing circuit in the inverters to see smoother value to help keep a smoother output sine wave.
Just my general theory, you are right that they don't alter the sine wave directly. Thus my theory that a center-tap auto-transformer, wired in parallel to the output circuit could help smooth out some harmonics caused by voltage and current fluctuations that could be possibly causing the inverters to react negatively via load adjustments where it is trying to maintain consistent sine wave. (I hope I'm articulating it in a decent fashion)
I'm no engineer either, just thinking it's possible, no concrete science I have to remember or reference my gut-based theory here, disclaimer, I am just some DIY wannabe hobbyist (with a little troubleshooting experience under my belt)..